Analytical models for the image Loève-Karhunen eigenfunctions (Q2718064)

The Loève-Karhunen expansion (LKE) has been frequently used to represent images by theirs compression. In this paper systems of eigenfunctions for the LKE are studied (the hypothesis is taken that an image is an element of a random field whose properties are contained in the associated autocovariance kernel). NEWLINENEWLINENEWLINEA new model for the covariance functions compatible with ``universal'' eigenfunctions is proposed. The eigenfunctions and eigenvalues are defined as ones of the Fredholm integral operator constructed in the form of an integral with a certain kernel along the image tessel. The case of one dimensional random processes and the case of circular symmetry are considered in details.